Answer
Please see the work below.
Work Step by Step
We know that
$\Delta S=\int ^{T_1}_{{T_{\circ}}}\frac{nC_{\circ}T_{\circ}dt}{T^2}dT$
$=nC_{\circ}T_{\circ}\int ^{T_1}_{{T_{\circ}}}\frac{1}{T^2}dT$
$=nC_{\circ}T_{\circ}\frac{T^{-2+1}}{-2+1}|^{T=T_1}_{T=T_{\circ}}$
$=nC_{\circ}T_{\circ}(\frac{-1}{T_1}+\frac{1}{T_{\circ}})$
$=\frac{nC_{\circ}(T_1-T_{\circ})}{T_1}$
